Erro retornado no console do navegador: 400 bad request
 
	Rastreei o erro ate essa parte no arquivo admin-ajax.php mudando o valor de resposta de 0 para 1:
 
if ( is_user_logged_in() ) {
	// If no action is registered, return a Bad Request response.
	if ( ! has_action( "wp_ajax_{$action}" ) ) {
		wp_die( '0', 400 );
	}
	Tentei de tudo, mas infelizmente nao entendi oq realmente significa esse login e como ele funciona.
 
	Vi algumas pessoas tendo problema com o host, no meu caso estou usando hostinger. (Nao creio que isso e relevante mas ta ai.)
 
	 
 
	Código utilizado: 
	 
 
	Javascript
 
function formValidation() {
	  event.preventDefault();
	  var name = document.forms["contactForm"]["name"].value;
	  var email = document.forms["contactForm"]["email"].value;
	  var subject = document.forms["contactForm"]["subject"].value;
	  var message = document.forms["contactForm"]["message"].value;
	  document.getElementById('status').innerHTML = '';
      var errorMessage="<span class='error'>All fields are required.</span>";
	  var regEx = /^([A-Za-z0-9_\-\.])+\@([A-Za-z0-9_\-\.])+\.([A-Za-z]{2,4})$/;
         if (name.trim() == "" ||email.trim() == "" || subject.trim() == "" || message.trim() == "") {
             document.getElementById('status').innerHTML = errorMessage;
             return false;
           }
       if (!regEx.test(email)) {
    	   var errorMessage="<span class='error'>Invalid email.</span>";
 		    document.getElementById('status').innerHTML = errorMessage;
 		    return false;
 		  }
	  processContactSubmit();
      return true;
	}
function processContactSubmit() {
                var request = new XMLHttpRequest();
                request.open("POST", "/wp-admin/admin-ajax.php?action=process_contact_form");
                request.onreadystatechange = function() {
                    if(this.readyState === 4 && this.status === 200) {
                        document.getElementById("status").innerHTML = this.responseText;
                    }
                };
                var myForm = document.getElementById("contactForm");
                var formData = new FormData(contactForm);
                request.send(formData);
}
	functions.php
 
	add_action('wp_ajax_nopriv_process_contact_form', 'process_contact_form');
    add_action('wp_ajax_process_contact_form', 'process_contact_form'); //Retirar essa parte para error no console, no contrario ira aparecer no navegador o numero 0.
    function process_contact_form() {
        $to = "Recipient Email Address";
        $subject = $_POST["subject"];
        $headers = "Testing";
        $message = $_POST["message"];
        $attachments = "";
        $sent = wp_mail($to, $subject, $message, $headers, $attachments);
        if (! $sent) {
            echo "<span class='error'>Problem in sending mail.</span>";
        } else {
            echo "<span class='success'>Hi, thank you for the message.</span>";
        }
        wp_die();
}
	Html
 
<form name="contactForm" id="contactForm" method="post" onsubmit="return formValidation()"  action="">
<p class="comment-form-comment"><textarea id="message" name="message" required="" placeholder="" aria-required="true"></textarea></p>
<p class="comment-form-author"><label for="author">Nome: </label> <input id="name" name="name" required="" size="30" type="text" value=" " /></p>
<p class="comment-form-author about"><label for="author">Assunto: </label> <input id="subject" name="subject" required="" size="40" type="text" value=" " /></p>
<p class="comment-form-email"><label for="email">Email: </label> <input id="email" name="email" required="" size="30" type="text" value="" /></p>
<p class="form-submit"><input id="submit" class="submit" name="email_contato" type="submit" value="Enviar" /></p>
</form> 
<h3><div id="status"></div></h3>